A sequence is defined by the formula f (n+1) = f (n) - 3. If f (4) = 22, what is f (1) ?

f (1) = 31

Step-by-step explanation:

since f (n+1) - f (n) = - 3

this sequence is arithmetic when the common diff is d = - 3

the general term is:

f (n) = f (1) + (n-1) d

put n = 4

f (4) = f (1) + (4-1) (-3)

22 = f (1) - 9

f (1) = 31